Three Dimensional MHD Simulations of Accretion to an Inclined Rotator: The "Cubed Sphere" Method

A. V. Koldoba; M. M. Romanova; G. V. Ustyugova; R. V. E. Lovelace

doi:10.1086/342780

paper

Three Dimensional MHD Simulations of Accretion to an Inclined Rotator: The "Cubed Sphere" Method

arXiv:astro-ph/0209598 · doi:10.1086/342780

Abstract

We describe a three-dimensional, Godunov-type numerical magnetohydrodynamics (MHD) method designed for studying disk accretion to a rotating magnetized star in the general case where the star's rotation axis, its magnetic moment, and the normal to the disk all have different directions. The numerical method uses a "cubed sphere" coordinate system which has advantages of Cartesian and spherical coordinate systems but does not have the singular axis ofthe spherical system. The grid is formed by a sequence of concentric spheres of radii $R_{j} \propto q^{j}$ with $j = 1.. N_{R}$ and $q = const > 1$ . The grid on the surface of the sphere consists of six sectors with the grid on each sector topologically equivalent to the equidistant grid on the face of a cube. Simulation results are discussed for the funnel flows (FF) to a star with dipole moment $\rvecmu$ at an angle $Θ = 3 0^{\circ}$ to the star's rotation axis $Ω$ which is aligned with the normal to the disk. Two important new 3D features are found in these simulations: (1) The funnel flow to the stellar surface is mainly in two streams which approach the star from opposite directions. (2) In the $x - z$ cross section of the flow containing $\rvecmu$ and $Ω$ , the funnel flow often takes the longer of the two possible paths along magnetic field lines to the surface of the star. A subsequent paper will give a detailed description of the method and results on 3D funnel flows at different inclination angles $Θ$ .

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Three Dimensional MHD Simulations of Accretion to an Inclined Rotator: The "Cubed Sphere" Method

Abstract

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